Review of Integrated Physics and Calculus by Andrew F. Rex and Martin Jackson

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln

Robert G. Fuller Publications and Presentations Research Papers in Physics and Astronomy

March 2001

Review of Integrated Physics and Calculus by Andrew F. Rex and Martin Jackson

Robert Fuller University of Nebraska - Lincoln, [email protected]

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Cosmology and Particle Astrophysics. Lars Bergstro¨m and tively shallow treatment of some topics, the references are Ariel Goobar. 344 pp. Wiley, New York, 1999. Price: quite meager: Along with a short list of other texts ͑and the $49.95 ͑paper͒ ISBN 0-471-97042-5. ͑Andrew H. Jaffe, research papers specifically cited͒, a list of good, modern Reviewer.͒ review articles to go along with each chapter would have been especially useful ͑perhaps the authors will consider With its constant influx of new and exciting data—and adding such a bibliography to the web site they dedicate to extensive coverage in daily newspapers—cosmology attracts the book͒. Also important to beginning students would be students with a wide range of education and research expe- some sense of the history of the field, as it slowly over the rience. Because of its recent transformation from a data- course of the 20th century achieved the status of a science in starved field to a data-driven one, any textbook attempting an its own right. overview of this subject is destined to be out-of-date soon For students with some knowledge of undergraduate phys- after its publication. ics and astrophysics, Cosmology and Particle Astrophysics Bergstro¨m and Goobar ͑not ‘‘Goodbar’’ as he is unfortu- provides a solid, concise introduction to the field. If paired nately referred to on the spine of the book!͒ have written an with a selection of topical reviews and research articles ͑for advanced undergraduate or beginning graduate text on the which this book should be adequate preparation͒, it would subject. One reason cosmology remains fun and exciting for offer a fine entree for students wishing to pursue research in its practitioner is that it requires ͑and rewards͒ understanding cosmology. of disparate fields of physics ͑radiative hydrodynamics, particle physics,...͒ and disparate physical situations ͑the hot and Andrew H. Jaffe is an Assistant Research Physicist at the dense early universe, the cold intergalactic medium, ...͒. Cos- University of California, Berkeley. He investigates the cosmology is a field for generalists, and much of the physics can mic microwave background, the growth of large-scale struc- indeed be understood at this level. ture, and other aspects of the history and evolution of the To keep the book both short and self-contained, the au- Universe. thors have made a number of choices which probably make it sufficient as the sole text for a class. On the other hand, this means that a large fraction of the book is spent develop- In the Shadow of the Bomb: Oppenheimer, Bethe, and ing general relativity, relativistic quantum mechanics, par- the Moral Responsibility of the Scientist. S. S. Schwe- ticle physics, and basic field theory. This space could have ber. 260 pp. Princeton U.P., Princeton, NJ, 2000. Price: been better spent concentrating on the core subjects of the $24.95 ISBN 0-691-04989-0. ͑Leo Sartori, Reviewer.͒ book ͑of 332 pages, 125 are devoted to this introductory material͒. In particular, I think short shrift has been given to the study of large-scale structure and the cosmic microwave J. Robert Oppenheimer and Hans Bethe are two of the background ͑my own subjects, admittedly͒, especially in leading figures in twentieth-century physics. Both played im- light of recent data in these fields. portant roles in the atomic bomb project and later advised the The authors were unlucky in their timing, as recent results US government on issues related to nuclear weapons. Op- from neutrino oscillation experiments, the MAXIMA and penheimer was the nation’s most influential scientist/ BOOMERANG CMB anisotropy experiments, as well as the politician during the immediate post-war period, but suffered 2DF and Sloan Digital Sky Survey, are in the midst of hon- a dramatic fall from grace, culminating in the revocation of ing our picture of the Universe. Perhaps naturally, the au- his security clearance after the infamous ‘‘trial’’ of 1954. thors go into greater depth on their own specialities: Berg- Bethe played a prominent part in the negotiations that led to stro¨m is an expert on the study of particle dark matter, and the Limited Test Ban Treaty and has long been an outspoken Goobar is a member of the Supernova Cosmology project, critic of ballistic missile defense. Now in his nineties, he one of the groups that has recently been responsible for ob- continues to contribute to the policy debate. Sam Schweber’s servations of the purported accelerating expansion of the new book provides mini-biographies of both men but focuses Universe. on their contrasting responses to the moral and political Compared to other recent cosmology texts ͑e.g., Kolb and questions posed by nuclear weapons. Turner’s The Early Universe, Peebles’ Principles of Physical The problem with the book is the marked asymmetry in Cosmology, Peacock’s Cosmological Physics, all from the the treatment of its two protagonists. In spite of its title, this late 80s or 90s and already somewhat out-of-date͒, Cosmol- is really a book about Bethe, whom the author has known ogy and Particle Astrophysics is less likely to be useful to intimately since he was his post-doc at Cornell in the early specialists as a reference—nor is it aimed at such an audi- 1950s; they co-authored the text from which many of my ence. Within its chosen scope, the book is clear, ͑very͒ con- generation learned about meson theory. Schweber has for cise, and fresh in its presentation, although the development some time been working on a full-scale biography of Bethe; of some topics is quite standard ͑in particular, the treatment the present book began as a chapter in that work. It is appar- of thermodynamics in an expanding universe closely mirrors ent that he admires Bethe greatly and has discussed with him the one given in Kolb and Turner’s Early Universe͒. in detail all the issues addressed in the book. The treatment However, it does lack some features that might have made of Oppenheimer is less authoritative and less satisfying, re- it a better introduction to the field. In addition to the rela- lying largely on Oppenheimer’s published words. Oppen-

394 Am. J. Phys. 69 ͑3͒, March 2001 http://ojps.aip.org/ajp/ © 2001 American Association of Physics Teachers 394 heimer, who died in 1967, was a charismatic and enigmatic In sum, this brief book whets my appetite for Schweber’s figure; after more than forty years, I can recall sitting in awed full biography of Bethe. I wish someone were doing a similar fascination at Institute seminars as he demolished one job for Oppenheimer. speaker after another. An authoritative biography of Oppen- heimer has yet to be written; I had hoped to learn more about Leo Sartori is Professor Emeritus of Physics at the Univer- him from this book. sity of Nebraska–Lincoln. He has a long-standing interest in Schweber attributes much of Oppenheimer’s intellectual issues of science and society. During the Carter administra- development and moral outlook to his early association with tion he served at the U.S. Arms Control and Disarmament Felix Adler’s Ethical Culture Society in New York City. The Agency and was an advisor to the SALT II delegation at book includes a lengthy digression on Adler and his society, Geneva. which, though informative, seems unnecessarily detailed for a work of this scope. For me, the most interesting portion of the book is the description of two national security cases involving physi- The Odd Quantum. Sam B. Treiman. 262 pp. Princeton cists, Philip Morrison and Bernard Peters, which were played U.P., Princeton, NJ, 1999. Price: $24.95 ISBN 0-691- out during the witch hunts of the late 1940s and early 50s. 00926-0. ͑Barry Holstein, Reviewer.͒ Bethe was involved in Morrison’s case and Oppenheimer in Peters’; both Morrison and Peters had been Oppenheimer’s When pressed to justify time and effort spent on research students at Berkeley. Bethe emerges in by far the superior activities, many of us have dusted off the old adage that the moral position. Morrison was a tenured associate professor at best researchers often make the best teachers. I realize that Cornell in 1951 when he came under fire for his involvement this is not always true, but it certainly was the case with the in leftist causes, which his attackers charged was damaging late Sam Treiman. Sam was an outstanding particle the University. The case dragged on for several years; in theorist—known among other things for the Goldberger– 1953 Morrison was grilled by Senator William Jenner’s In- Treiman relation, the Callan–Treiman equation, the ternal Security Subcommittee. Throughout the long ordeal Treiman–Yang angle, the Khuri–Treiman equations—as Bethe worked diligently with Morrison and University ad- well as for the fine group of students he produced—including ministrators to find a compromise solution that would protect Steve Weinberg, Steve Adler, Curt Callan, Glennys Farrar, Morrison’s academic freedom while meeting the Universi- etc. He was also a classroom star. When I was a postdoc at ty’s concerns. Princeton during the late 1960’s I had the privilege of work- Oppenheimer, by contrast, provided damaging testimony ing with him, and while I never took one of his classes, I against Peters during an interrogation by the security chief at used to hear the students describe his quantum mechanics Los Alamos and later at a closed session of the notorious course in reverential terms as a ‘‘classic.’’ This legendary House Committee on Un-American Activities. He described classroom prowess was recognized by the AAPT when in Peters as ‘‘a crazy person,’’ ‘‘quite red,’’ and ‘‘truly danger- 1985 Treiman was honored as the recipient of the Oersted ous,’’ a characterization that was entirely unwarranted. medal ͓Am. J. Phys. 53, 817 ͑1985͔͒. When news of Oppenheimer’s testimony leaked, many of his In the book The Odd Quantum, completed just before his close friends, including Bethe, were appalled and told him untimely death last year, Treiman describes quantum me- so. Although the University of Rochester, to its credit, did chanics, not in the mathematically precise form given in his not fire Peters and even promoted him to full professor, the graduate course, but rather in the style in which he gave an State Department withdrew his passport; unable to continue introductory and descriptive set of lectures to a group of his cosmic-ray research, which required foreign travel, he Princeton freshman in an honors course. ͑Warning: Princeton felt compelled to leave the country. Schweber provides many being Princeton, there is enough mathematics in this volume illuminating details concerning both cases. As he notes, Op- to scare away the standard freshman in most universities— penheimer was in a much more vulnerable situation than was certainly mine!͒ What results is a concise and beautifully Bethe because of his own leftist associations dating back to written summary of an expert’s view of the subject. the 1930s. Still, his denunciation of Peters seems inexcusable The first few chapters are fairly standard and are included and is undeniably a blot in his record. in order to bring the reader up to speed. However, since the The chapter on nuclear weapons policy contains some entire subject is covered in only a little over 250 pages, the well-known material on the history of the atomic and hydro- author is forced to skim over a great deal of material. Thus gen bomb projects, but is largely devoted to an exposition of after a brief first chapter in which he introduces the historical Bethe’s views on the hydrogen bomb. He at first opposed the background and some of the basic concepts to be considered, development of the H-bomb on moral grounds; that was also in the thirty pages of Chapter 2 he discusses classical me- the position of the General Advisory Committee of the AEC, chanics, electricity and magnetism, and special relativity. which Oppenheimer chaired. At the time, it was not at all Treiman is not afraid to introduce basic mathematics ͑includ- clear that a fusion weapon could be made to work. After Stan ing partial derivatives͒, and this will definitely intimidate Ulam and Edward Teller had shown that it was indeed fea- some readers. sible, Bethe reluctantly concluded that the United States had After a chapter in which he outlines what is generally to develop the bomb because the Russians were likely to do called ‘‘modern physics’’—including blackbody radiation, so. He helped design the weapon even though he believed it the Rutherford atom, the Bohr model, etc.—he finally gets was a ‘‘terrible error,’’ and publicly urged that the United into quantum mechanics in Chapter 4. Eschewing watering States pledge that it would never be the first to use one. In down the subject, after a brief discussion of two-slit scatter- 1983 he voiced his regrets, declaring that ‘‘we would now be ing he goes right to the Schro¨dinger equation, and discusses very much better off if the hydrogen bomb had never been the meaning of the wave function, operator notation, com- invented.’’ mutation relations, the uncertainty principle, tunneling,

395 Am. J. Phys., Vol. 69, No. 3, March 2001 Book Reviews 395 etc.—it’s all there. Then in Chapter 5 he summarizes some plagues those who have tried to evade quantum mechanical of the classic quantum mechanical problems—the free par- behavior by postulating unknown hidden variables which, ticle, harmonic oscillator, hydrogen atom ͑including fine and were they known, would resolve mysteries such as the EPR hyperfine structures͒, a variant of the Bohm–Aharonov ef- phenomenon. However, the experimental exclusion of Bell’s fect, and alpha decay. These are enjoyable for a physicist to inequalities shows that this is definitely not the case. Any read, but again I wonder about the novice. local manifestation of hidden variables is ruled out by such The next two chapters—on identical particles and on measurements. ‘‘What’s going on?’’—are for my money the most interest- The volume closes with a chapter on building blocks and ing in the book. Both deal with essential ways in which then one on quantum field theory. The former is fairly stan- quantum mechanics differs from its familiar classical limit. It dard and chronicles the fundamental fermions ͑quarks, lep- is tempting to try to understand quantum phenomena from tons͒ and bosons (WϮ,Z0,␥), together with their interactions our classical experience, but this is difficult because quantum and basic symmetries—parity, charge conjugation, time re- mechanics really is different. One manifestation of this fact versal, etc. The ideas of gauge theory and the standard model is how identical particles are treated in the two regimes. In are developed. The chapter on quantum field theory ͑QFT͒, classical mechanics, particles can be identical, but it really however, is unusual in that in words and pictures ͑well, makes little difference, because we could in principle follow Feynman diagrams͒ Treiman shows how QFT, which of ne- their motion ͑though the huckster moves the shells more rap- cessity involves creation and destruction of quanta, is able to idly than the eye can follow, the pea is definitely under one account for the myriad of processes seen in nature. In par- shell and this is in principle determinable͒. On the other ticular he makes the connection between the eigenstates of hand, in quantum mechanics identical particles are utterly free field theory ͑states consisting of 0,1,2,... noninteracting identical. The presence of a particle is indicated only by a quanta͒ with the identical particles seen in nature. The exis- peak in ͉␺͉2 and there exists no conceivable way to distin- tence of precisely identical and indistinguishable copies of guish one electron from its wave function partner. Treiman fermions and bosons, with their attendant significance for notes that this fact has deep and far-reaching consequences. quantum mechanics, is required by the validity of QFT. This There exist two possibilities for identical particle wave field-theoretic description requires the constant creation/ functions—one antisymmetric under interchange of particle destruction of identical real and virtual quanta, and it is this identities and the other symmetric. ͑Only these choices are continual resewing of the fabric in which our world is possible because two interchanges bring us back to where we clothed that is responsible for its marvelous variety. On the started.͒ By the spin-statistics theorem, the former ͑latter͒ is other hand, Treiman acknowledges in closing that while QFT associated with fermions ͑bosons͒ carrying half-integral ͑in- provides an excellent description of nature, it really does not tegral͒ spin. The Pauli exclusion principle, which follows explain why things are as they are. from the antisymmetry of the fermion wave function, leads Summarizing, although I am not particularly sanguine ͑ to the remarkably different chemical properties of neighbor- about the utility of the volume for beginning students out- ͒ ing elements on the periodic table. In a world where elec- side Princeton , this book is a good read for those of us who trons were bosons, the hydrogen and helium atoms ͑and in- already know quantum mechanics and wish to understand it deed all others͒ would be very similar, since every electron more deeply, or for technically able readers who wish to could ͑and would͒ occupy the ground state orbital preferen- know some of the intriguing aspects and beauty of the sub- tially. Thus it could be said that the quantum mechanical ject. property associated with particle identity is responsible for the world as we know it and for life itself! On the boson side Barry R. Holstein is Professor of Physics at the University of such simultaneous occupation of the ground state energy lev- Massachusetts at Amherst. Besides being a frequent con- els allows for the existence of phenomena such as supercon- tributor to this journal he is active as a particle/nuclear ductivity, superfluidity, etc., and Treiman also makes refer- theorist, and has published papers with Sam Treiman (and ence to the au courant topic of Bose–Einstein condensation. others) on symmetry issues, especially those which probe the ͑Surprisingly, he omits stimulated emission topics such as fundamental structure of the electroweak interaction. lasers or masers, however.͒ The brief chapter titled ‘‘What’s going on?’’ also rewards a careful reading. In it the author explores the essence of quantum/classical differences, with discussions of double-slit Integrated Physics and Calculus. Andrew F. Rex and Mar- scattering, Schro¨dinger’s cat, the Einstein–Podolsky–Rosen tin Jackson. 592 pp. ͑Vol. I͒, 608 pp. ͑Vol. II͒. ͑EPR͒ paradox, and Bell’s inequalities. Though terse, the Addison–Wesley, San Francisco, CA, 2000. Price: discussion here is among the best I have seen. Treiman $45.00 per volume ͑paper͒ ISBN 0-201-47396-8, 0-201- stresses that all of us in our daily existence are quantum 47397-6. ͑Robert G. Fuller, Reviewer.͒ mechanical cats—to an outside observer, we are all superpo- sitions until an observation is made. On the EPR paradox Are you ready to try something that seems obvious and yet Treiman notes that ‘‘One has to say simply ͑though it is is innovative? If so, then maybe you are ready to teach a rarely said simply͒ that the EPR notion of physical reality is combined physics and calculus course. In fact, many of us too demanding for the quantum world we actually inhabit.’’ who have been teaching calculus-based physics have always And he does say it simply, pointing out that even though via felt that we had to teach both physics and calculus, because EPR we can predict the spin of a remote system with abso- our students seemed to be unable to do anything we thought lute certainty, this does not indicate that it is a classical sys- they had learned to do in the prerequisite calculus course͑s͒. tem. What breaks down here is that in this sense quantum Now, at last, a courageous physicist and mathematician mechanics is nonlocal, and this is an essential feature that have worked together to create a combined physics and cal- does not exist in classical mechanics. The same problem culus textbook. Professors Rex and Jackson have written a

396 Am. J. Phys., Vol. 69, No. 3, March 2001 Book Reviews 396 textbook for such a combined course based on their teaching after the students take several semesters of calculus before experiences at the University of Puget Sound since 1994. I studying differential equations? have struggled with my own versions of such a course at two What a joy it was to teach simple harmonic motion just different institutions, with different mathematicians. The after the students had studied Taylor’s theorem in mathemat- Rex/Jackson text would have saved us immense headaches. ics! I was able to give my thrilling ‘‘all systems are simple This text follows a very traditional sequence of physics harmonic’’ lecture to a class of believers, instead of the typi- topics while building in the calculus concepts as they are cal classroom full of blank stares when the words ‘‘Taylor needed for the physics. For example, differential equations series’’ are mentioned. The Rex/Jackson text can enable you are introduced along with the applications of Newton’s sec- to have the same joyful experience. Their presentation of ond law. Line integrals are taught in the chapter with work sequences and series, including the Taylor series, Chapter done by a variable force. In the second volume, partial de- 11, Section 6, just precedes the Oscillations and Second- rivatives and gradients are included in the chapter on electric Order Differential Equations, Chapter 12. potential. This text includes a variety of math and physics The calculus reform movement has created, in my opin- problems at the end of each chapter and has the answers to ion, mathematics departments around the country that are most odd-number problems in the back of the books. The willing to explore very different sequences of calculus topics problems are arranged by sections of the book and include a and may be willing to work with you to co-teach a course good variety of mathematical and physical problems. I wish using the Rex/Jackson text. A calculus-reformed mathemat- they would add a collection of multiple concept problems, ics faculty should welcome this text. not directly associated with a particular section of the book, I believe this is one direction for the next important phys- to challenge students to ﬁgure out what mathematics and ics curriculum reform movement to go. I encourage you to physics concepts to use to solve the problems. But an in- try the Rex/Jackson approach to breathing some new life into structor can add his or her own context-rich problems as the calculus-based physics courses at your institution. Using desired. this text in your course can foster a new understanding of The Rex/Jackson approach matches quite closely the ap- calculus as the ‘‘language of physics’’ that was so important proach I successfully tried when co-teaching with a math- in Newton’s development of calculus. ematician, but our students had two different textbooks, one Try letting the Rex/Jackson textbook lead you into the on physics and another on calculus. The two textbooks had thrilling experience of teaching a physics course integrated different approaches and different notations, stumbling with calculus. I think you will like it. blocks for the students. This book would have helped our students considerably. The Rex/Jackson text uses Newton’s second law ͑Chapter Robert G. Fuller is professor of physics and director of the 5͒ as a motivation for introducing differential equations research in physics education group at the University of ͑Chapters 6.1 and 6.2͒. Then they use differential equations Nebraska–Lincoln. He has taught using the Keller Plan, to study more applications of Newton’s second law ͑Chapter Piagetian-based instruction, Karplus learning cycles, inter- 6.3͒. Doesn’t this seem more reasonable than waiting until active videodiscs, and ‘‘paperless’’ physics.

BOOKS RECEIVED

Academic Excellence: The Role of Research in the Physical Sciences at Essentials of Electromagnetics for Engineering. David A. de Wolf. 509 Undergraduate Institutions. Edited by Michael P. Doyle. 199 pp. Re- pp. Cambridge U.P., New York, 2001. Price: $69.95 ISBN 0-521- search Corporation, Tucson, AZ, 2000. Price: $3.00 ISBN 0-9633504- 66281-8. 5-5. Explicit Birational Geometry of 3-Folds. Edited by Alessio Corti and Advances in Chemical Physics, Vol. 114. Edited by I. Prigogine and Stu- Miles Reid. 349 pp. Cambridge U.P., New York, 2000. Price: $44.95 art A. Rice. 630 pp. Wiley, New York, 2000. Price not given, ISBN ͑paper͒ ISBN 0-521-63641-8. 0-471-39267-7. The Foundations of Newtonian Scholarship. Edited by Richard H. Dalitz Advances in Chemical Physics, Vol. 115. Edited by I. Prigogine and Stu- and Michael Nauenberg. 242 pp. World Scientific, River Edge, NJ, art A. Rice. 441 pp. Wiley, New York, 2000. Price not given, ISBN 2000. Price: $60.00 ISBN 981-02-3920-3. 0-471-39331-2. Fundamentals of Carrier Transport, 2nd ed. Mark Lundstrom. 418 pp. The Bit and the Pendulum: From Quantum Computing to M Theory— Cambridge U.P., New York, 1990, 2000. Price: $59.95 ISBN 0-521- The New Physics of Information ͑paperback edition͒. Tom Siegfried. 63134-3. 281 pp. Wiley, New York, 1999, 2000. Price: $15.95 ͑paper͒ ISBN Instructor’s Manual: Fundamentals of Ethics for Scientists and Engi- 0-471-39974-4. neers. Edmund G. Seebauer and Robert L. Barry. 176 pp. Oxford U.P., Data Analysis Techniques for High-Energy Physics, 2nd ed. R. Fru¨h- New York, 2001. Price not given ͑paper͒ ISBN 0-19-514419-8. wirth et al. 384 pp. Cambridge U.P., New York, 1990, 2000. Price: Introduction to Partial Differential Equations ͑reprint͒. Donald $120.00 ͑cloth͒ ISBN 0-521-63219-6; $54.95 ͑paper͒ ISBN 0-521- Greenspan. 195 pp. Dover, Mineola, NY, 1961, 2000. Price: $8.95 ͑pa- 63548-9. per͒ ISBN 0-486-41450-7. Diffusion and Reactions in Fractals and Disordered Systems. Daniel Introduction to the Replica Theory of Disordered Statistical Systems. ben-Avraham and Shlomo Havlin. 316 pp. Cambridge U.P., New York, Viktor Dotsenko. 220 pp. Cambridge U.P., New York, 2001. Price: 2000. Price: $90.00 ISBN 0-521-62278-6. $74.95 ISBN 0-521-77340-7. Einstein, Physics and Reality. Jagdish Mehra. 156 pp. World Scientific, Introduction to Surface and Thin Film Processes. John A. Venables. 372 River Edge, NJ, 1999. Price: $32.00 ISBN 981-02-3913-0. pp. Cambridge U.P., New York, 2000. Price: $110.00 ͑cloth͒ ISBN El Ninõ and the Southern Oscillation: Multiscale Variability and Global 0-521-62460-6; $39.95 ͑paper͒ ISBN 0-521-78500-6. and Regional Impacts. Edited by Henry F. Diaz and Vera Markgraf. Mass Transport in Solids and Fluids. David S. Wilkinson. 270 pp. Cam- 496 pp. Cambridge U.P., New York, 2000. Price: $90.00 ISBN 0-521- bridge U.P., New York, 2000. Price: $110.00 ͑cloth͒ ISBN 0-521- 62138-0. 62409-6; $39.95 ͑paper͒ ISBN 0-521-62494-0.

397 Am. J. Phys., Vol. 69, No. 3, March 2001 Book Reviews 397 Mathematical Modeling in Continuum Mechanics. Roger Temam and Quantum Computation and Quantum Information. Michael A. Nielsen Alain Miranville. 288 pp. Cambridge U.P., New York, 2000. Price: and Isaac L. Chuang. 676 pp. Cambridge U.P., New York, 2000. Price: $54.95 ISBN 0-521-64362-7. $130.00 ͑cloth͒ ISBN 0-521-63235-8; $47.95 ͑paper͒ ISBN 0-521- Mechanics, Heat, and the Human Body: An Introduction to Physics. 63503-9. Howard D. Goldick. 212 pp. Prentice Hall, Upper Saddle River, NJ, Quantum Evolution: An Introduction to Time-Dependent Quantum ͑ ͒ 2001. Price not given paper ISBN 0-13-922816-0. Mechanics. James E. Bayfield. 386 pp. Wiley, New York, 1999. Price: Microhardness of Polymers. F. J. Balta´ Calleja and S. Fakirov. 237 pp. $99.95 ISBN 0-471-18174-9. Cambridge U.P., New York, 2000. Price: $95.00 ISBN 0-521-64218-3. Raman Spectroscopy for Chemical Analysis. Richard L. McCreery. 420 A Modern Introduction to Particle Physics, 2nd ed. Fayyazuddin and Riazuddin. 717 pp. World Scientific, River Edge, NJ, 1992, 2000. pp. Wiley, New York, 2000. Price: $99.95 ISBN 0-471-25287-5. Price: $99.00 ISBN 981-02-3876-2. The Runaway Universe: The Race to Find the Future of the Cosmos. Modern Mathematical Methods for Physicists and Engineers. C. D. Donald Goldsmith. 232 pp. Perseus, Cambridge, MA, 2000. Price: Cantrell. 763 pp. Cambridge U.P., New York, 2000. Price: $120.00 $16.00 ͑paper͒ ISBN 0-7382-0429-3. ͑cloth͒ ISBN 0-521-59180-5; $49.95 ͑paper͒ ISBN 0-521-59827-3. Scattering of Waves from Large Spheres. Walter T. Grandy, Jr. 370 pp. Mother Nature’s Two Laws: Ringmasters for Circus Earth. Lessons on Cambridge U.P., New York, 2000. Price: $95.00 ISBN 0-521-66126-9. Entropy, Energy, Critical Thinking, and the Practice of Science. A. Selected Papers of Richard Feynman, with Commentary. Edited by D. Kirwan, Jr. 173 pp. World Scientific, River Edge, NJ, 2000. Price: Laurie M. Brown. 999 pp. World Scientific, River Edge, NJ, 2000. $28.00 ISBN 981-02-4314-6. Price: $96.00 ISBN 981-02-4130-5. ͑ ͒ The Nature of Space and Time paperback edition . Stephen Hawking and Smart Structures: Analysis and Design. A. V. Srinivasan and D. Michael Roger Penrose. 141 pp. Princeton U.P., Princeton, NJ, 1996, 2000. McFarland. 228 pp. Cambridge U.P., New York, 2001. Price: $95.00 ͑ ͒ Price: $14.95 paper ISBN 0-691-05084-8. ͑cloth͒ ISBN 0-521-65026-7; $34.95 ͑paper͒ ISBN 0-521-65977-9. Numerical Simulation of Reactive Flow, 2nd ed. Elaine S. Oran and Jay Theory of Satellite Geodesy: Applications of Satellites to Geodesy ͑re- P. Boris. 529 pp. Cambridge U.P., New York, 1987, 2001. Price: print͒. William M. Kaula. 124 pp. Dover, Mineola, NY, 1966, 2000. $90.00 ISBN 0-521-58175-3. ͑ ͒ The Physics of Consciousness: The Quantum Mind and the Meaning of Price: $7.95 paper ISBN 0-486-41465-5. Life. Evan Harris Walker. 368 pp. Perseus, Cambridge, MA, 2000. Turbulent Flows. Stephen B. Pope. 771 pp. Cambridge U.P., New York, ͑ ͒ ͑ ͒ Price: $17.00 ͑paper͒ ISBN 0-7382-0436-6. 2000. Price: $130.00 cloth ISBN 0-521-59125-2; $49.95 paper The Physics of Information Technology. Neil Gershenfeld. 370 pp. Cam- ISBN 0-521-59886-9. bridge U.P., New York, 2000. Price: $39.95 ISBN 0-521-58044-7. Wonders of Numbers: Adventures in Mathematics, Mind, and Mean- The Pursuit of Destiny: A History of Prediction. Paul Halpern. 250 pp. ing. Clifford A. Pickover. 396 pp. Oxford U.P., New York, 2001. Perseus, Cambridge, MA, 2000. Price: $25.00 ISBN 0-7382-0095-6. Price: $27.50 ISBN 0-19-513342-0.

INDEX TO ADVERTISERS

Cambridge University Press ...... Inside Front Cover Physics Academic Software ...... 242 Project CLEA ...... 241 Science Job Market...... 241 WebAssign ...... 239

398 Am. J. Phys., Vol. 69, No. 3, March 2001 Book Reviews 398